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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9207
Title: Optimum runge-kutta fehlberg methods for first order differential equations
Authors: Jain R.K.
Jain M.K.
Published in: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Abstract: The optimum Runge-Kutta method of a particular order is the one whose truncation error is minimum. In this paper we have derived optimum Runge-Kutta methods of 0(hm+4), 0(hm+5) and 0(hm+6) for m = 0(1)8 based on the Fehlberg transformation. These methods require two, three and four evaluations of f¯(x,y¯), per step, for the differential equation y¯′=f¯(x,y). The region of stability in the complex plane has been obtained and is found to increase with m. The convergence of these methods to the exact solution has been proved. The numerical solution of one example obtained with these methods have been compared with the exact solution and with that obtained by using the classical Runge-Kutta and the Fehlberg methods. It has been assumed that f¯(x,y¯) is sufficiently differentiable in the entire region of integration. © 1971 by Academic Press Inc. (London) Limited.
Citation: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) (1971), 8(3): 386-396
URI: https://doi.org/10.1093/imamat/8.3.386
http://repository.iitr.ac.in/handle/123456789/9207
Issue Date: 1971
ISSN: 2724960
Author Scopus IDs: 26659438700
56226587200
Author Affiliations: Jain, R.K., Department of Mathematics, University of Saskatchewan, Saskatoon, Canada
Jain, M.K., Department of Mathematics, Indian Institute of Technology, Delhi, India
Corresponding Author: Jain, R.K.; Department of Mathematics, University of Saskatchewan, Saskatoon, Canada
Appears in Collections:Journal Publications [HY]

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